Input‐To‐State Stable Tracking Control Design for Fully Actuated Mechanical Systems Using Position Measurements Only

ABSTRACT In this article, we consider tracking control design for fully actuated mechanical systems using position measurements only. A recently developed hybrid momentum observer is used, which has the property that the momentum estimation error is a passive output from the estimation error dynamics. To complement this, a tracking error system is constructed with error coordinates defined between the momentum estimate and the desired momentum. The tracking error dynamics are similarly passive with the momentum estimation error as the passive input to the tracking error system. Exploiting the passivity of both the observer and tracking controller subsystems, a passive interconnection is constructed which results in a storage function for the joint observer and controller systems. It is shown that the joint system is Input‐to‐State Stable (ISS) with respect to external disturbances and the effect of the disturbance can be attenuated via tuning gains. The results are numerically demonstrated on a 2‐link manipulator system.